Ondalık Sayıdan Kesre Çevirici – Sadeleştirilmiş
Herhangi bir ondalık sayıyı sadeştirilmiş kesre çevirin. Adım adım süreci gösterir.
Nasıl to Dönüştür a Ondalık to a Kesir
To dönüştür a ondalık to a kesir:
- Count the ondalık places (e.g., 0.75 has 2 ondalık places)
- Write the ondalık as a kesir over 10^n (e.g., 75/100)
- Simplify using the Greatest Common Divisor (GCD) → 75/100 = 3/4
Our hesaplayıcı does all three steps automatically and shows the sonuç in lowest terms.
Common Ondalık to Kesir Equivalents
| Decimal | Fraction |
|---|---|
| 0.1 | 1/10 |
| 0.125 | 1/8 |
| 0.25 | 1/4 |
| 0.333... | 1/3 |
| 0.5 | 1/2 |
| 0.666... | 2/3 |
| 0.75 | 3/4 |
| 0.875 | 7/8 |
Ne is the GCD?
The Greatest Common Divisor (GCD) is the largest Sayı that divides both the numerator and denominator without remainder. Dividing both by the GCD simplifies the kesir to its lowest terms.
For örnek, GCD(75, 100) = 25. So 75/100 ÷ 25/25 = 3/4. The Euclidean algorithm is the standard efficient method: GCD(a, b) = GCD(b, a mod b) until b = 0.
Sık Sorulan Sorular
Nasıl do I dönüştür a repeating ondalık to a kesir?
For a repeating ondalık like 0.333..., set x = 0.333..., then 10x = 3.333..., subtract: 9x = 3, so x = 3/9 = 1/3. For 0.142857142857... (repeating 6 digits), the process requires multiplying by 10^6.
Ne is the kesir for 0.625?
0.625 = 625/1000. GCD(625, 1000) = 125. So 625/1000 ÷ 125/125 = 5/8. Bu nedenle 0.625 = 5/8.
Can all decimals be expressed as fractions?
Terminating decimals (like 0.75) and repeating decimals (like 0.333...) can always be written as fractions. Non-repeating, non-terminating decimals (like π = 3.14159...) are irrational and cannot be expressed as exact fractions.